Equipment looted from enemies in Rebirth Mode have boosted attributes based on the player's current Orb Rank. The purpose of looted gear is to act as a bridge between unlocking Tier 2/3 Rebirth Shop gear, provide alternate paths of power, and keep looted gear somewhat relevant for early-rank orb gardens.
Depending on rank, a character will get 2-4 attribute rolls, each of which are applied to one of the equipment's existing attributes. The boost amount is also dependent on that character's rank.
A boost amount is based on the attribute's existing base value, calculated as 25% of the base value plus ten. That boost amount is scaled by the player's rank, plus 0.5% per rank up to rank 100. In essence, for each existing stat we calculate that stat's boost amount.
base = stat / 4 + 10
boost = base + base * min(rank, 100) / 200
For example, Deathfalchion has 60 base attack. It's attack boost value would be 25 at rank 0 and 37 at rank 100 and beyond. Each attribute gets its own boost value.
Once the boost amounts are calculated, an existing attribute on the equipment is chosen at random and increased based on its base value. This is repeated for a certain number of rolls. The number of rolls is calculated as 2 plus the player's rank divided by 35.
rolls = 2 + min(rank, 100) / 35
Continuing the Deathfalchion example, assuming rank 100 we get 4 total rolls. The boost amount is 37 attack with a base attribute of 60 attack, so a theoretical max attack on this weapon is 208. (60 + 37 * 4). Since Deathfalchion has two attributes (attack and crit) the probability of a Deathfalchion drop having max attack is 1/16.